Problem: Simplify the following expression: $ r = \dfrac{-2}{7} + \dfrac{-5p - 1}{5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-2}{7} \times \dfrac{5}{5} = \dfrac{-10}{35} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-5p - 1}{5} \times \dfrac{7}{7} = \dfrac{-35p - 7}{35} $ Therefore $ r = \dfrac{-10}{35} + \dfrac{-35p - 7}{35} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-10 - 35p - 7}{35} $ $r = \dfrac{-35p - 17}{35}$